Math 156     Applied Honors Calculus II    Topics
               Lecture notes will be provided on the course website, but students may also consult the
               following books (or any other calculus textbook).
               1. “Calculus II” by Jerrold Marsden and Alan Weinstein, Springer
               available for free at the Caltech website
               https://www.cds.caltech.edu/ marsden/volume/Calculus/
                                                 ~
               2. “Calculus” by James Stewart, Cengage
               Topics
                Part 1. Integration                            Marsden-Weinstein    Stewart (5th edition)
                1.1 sigma notation                             4.1                  App. E
                1.2 area                                       4.2                  5.1
                1.3 definite integral                           4.3                  5.2
                1.4 fundamental theorem of calculus            4.4, 4.5             5.3, 5.4
                1.5 work                                       9.5                  6.4
                1.6 improper integrals                         11.3                 8.8
                1.7 arclength                                  10.3                 9.1
                1.8 surface area                               10.3                 9.2
                1.9 center of mass                             9.4                  9.3
                1.10 probability density functions                                  9.5
                Review as needed.
                R.1 substitution                               7.2                  5.5
                R.2 integration by parts                       7.4                  8.1
                R.3 trigonometric substitution                 10.1                 8.2, 8.3
                R.4 partial fractions                          10.2                 8.4
                R.5 hyperbolic functions                       8.3                  7.6
                R.6 L’Hˆopital’s rule                          11.2                 7.7
                Part 2. Differential Equations
                2.1 1st order equations                        8.2                  10.1
                2.2 exponential growth/decay                   8.2                  10.3, 10.4
                2.3 logistic equation                          8.5                  10.5
                2.4 Euler’s method                             8.5                  10.2
                Part 3. Series
                3.1 sequences                                  11.4                 12.1
                3.2 series                                     12.1                 12.2
                3.3 convergence tests (integral, comparison)   12.2, 12.3           12.3, 12.4
                3.4 alternating series                         12.2                 12.5
                3.5 ratio test                                 12.3                 12.6
                3.6 power series                               12.4                 12.8, 12.9
                3.7 Taylor series                              12.5                 12.10, 12.11
                3.8 binomial series                            12.5                 12.12
                Additional Topics (time permitting)
                A.1 parametric curves                          10.4                 11.1
                A.2 arclength and area in polar coordinates    10.5                 11.2, 11.3
                A.3 complex numbers                            12.6                 App. G
                A.4 2nd order equations, oscillations          8.1                  18.1, 18.2, 18.3